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Таблица истинности ONLINE
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Таблица истинности для функции (A∧(¬A∨¬D)∧A)∧((B∧(D∧(¬D∨C)))∨(C∨A)∨(D∨¬A)):
Промежуточные таблицы истинности:¬A: ¬D: (¬A)∨(¬D): | A | D | ¬A | ¬D | (¬A)∨(¬D) | | 0 | 0 | 1 | 1 | 1 | | 0 | 1 | 1 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 |
A∧((¬A)∨(¬D)): | A | D | ¬A | ¬D | (¬A)∨(¬D) | A∧((¬A)∨(¬D)) | | 0 | 0 | 1 | 1 | 1 | 0 | | 0 | 1 | 1 | 0 | 1 | 0 | | 1 | 0 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 |
(A∧((¬A)∨(¬D)))∧A: | A | D | ¬A | ¬D | (¬A)∨(¬D) | A∧((¬A)∨(¬D)) | (A∧((¬A)∨(¬D)))∧A | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | 1 | 0 | 0 | | 1 | 0 | 0 | 1 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
(¬D)∨C: | D | C | ¬D | (¬D)∨C | | 0 | 0 | 1 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 1 | 0 | 1 |
D∧((¬D)∨C): | D | C | ¬D | (¬D)∨C | D∧((¬D)∨C) | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 0 | | 1 | 1 | 0 | 1 | 1 |
B∧(D∧((¬D)∨C)): | B | D | C | ¬D | (¬D)∨C | D∧((¬D)∨C) | B∧(D∧((¬D)∨C)) | | 0 | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | | 0 | 1 | 0 | 0 | 0 | 0 | 0 | | 0 | 1 | 1 | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 1 | 1 | 0 | 0 | | 1 | 0 | 1 | 1 | 1 | 0 | 0 | | 1 | 1 | 0 | 0 | 0 | 0 | 0 | | 1 | 1 | 1 | 0 | 1 | 1 | 1 |
C∨A: D∨(¬A): | D | A | ¬A | D∨(¬A) | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 |
(B∧(D∧((¬D)∨C)))∨(C∨A): | B | D | C | A | ¬D | (¬D)∨C | D∧((¬D)∨C) | B∧(D∧((¬D)∨C)) | C∨A | (B∧(D∧((¬D)∨C)))∨(C∨A) | | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
((B∧(D∧((¬D)∨C)))∨(C∨A))∨(D∨(¬A)): | B | D | C | A | ¬D | (¬D)∨C | D∧((¬D)∨C) | B∧(D∧((¬D)∨C)) | C∨A | (B∧(D∧((¬D)∨C)))∨(C∨A) | ¬A | D∨(¬A) | ((B∧(D∧((¬D)∨C)))∨(C∨A))∨(D∨(¬A)) | | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
((A∧((¬A)∨(¬D)))∧A)∧(((B∧(D∧((¬D)∨C)))∨(C∨A))∨(D∨(¬A))): | A | D | B | C | ¬A | ¬D | (¬A)∨(¬D) | A∧((¬A)∨(¬D)) | (A∧((¬A)∨(¬D)))∧A | ¬D | (¬D)∨C | D∧((¬D)∨C) | B∧(D∧((¬D)∨C)) | C∨A | (B∧(D∧((¬D)∨C)))∨(C∨A) | ¬A | D∨(¬A) | ((B∧(D∧((¬D)∨C)))∨(C∨A))∨(D∨(¬A)) | ((A∧((¬A)∨(¬D)))∧A)∧(((B∧(D∧((¬D)∨C)))∨(C∨A))∨(D∨(¬A))) | | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 |
Общая таблица истинности:| A | D | B | C | ¬A | ¬D | (¬A)∨(¬D) | A∧((¬A)∨(¬D)) | (A∧((¬A)∨(¬D)))∧A | (¬D)∨C | D∧((¬D)∨C) | B∧(D∧((¬D)∨C)) | C∨A | D∨(¬A) | (B∧(D∧((¬D)∨C)))∨(C∨A) | ((B∧(D∧((¬D)∨C)))∨(C∨A))∨(D∨(¬A)) | (A∧(¬A∨¬D)∧A)∧((B∧(D∧(¬D∨C)))∨(C∨A)∨(D∨¬A)) | | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности: | A | D | B | C | F | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 0 | 1 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | | 1 | 1 | 0 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | 0 |
F сднф = A∧¬D∧¬B∧¬C ∨ A∧¬D∧¬B∧C ∨ A∧¬D∧B∧¬C ∨ A∧¬D∧B∧C Логическая cхема:
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